Intertemporal Substitution, Imports and Permanent-Income

Jamal of INW3NAUONAL ECONOMlCS ELSEYIER Journal of International Economics 40 (1996) 439-457 Intertemporal substitution, imports and the permanent income model Robert A. Amanoa’*, Tony S. Wirjantob “Research Department, Bank of Canada, 234 Wellington Street, Ottawa, Ontario, KlA OG9. Canada hDepartment of Economics, University of Waterloo, Waterloo, Ontario, N2L 3GI, Canada Received 29 November 1994: revised 15 October 1995 Abstract We examine the importance of intertemporal substitution in U.S. import consumption using a model of permanent income that allows for random preference shocks and additive separability. The latter feature allows us to take two estimation approaches. In the first approach, we show that there is a cointegrating restriction imposed by the first-order conditions of the model which allows us to estimate the intertemporal elasticity of imported and domestic goods consumption. In the second approach, we estimate the Euler equations using generalized method of moments. This approach, however, requires us to place some restrictive assumptions on the model that are not required for the first estimation approach. Thus, the two different approaches allow an assessment of the severity of these restrictive assumptions which are often imposed in the literature. Key words: Intertemporal elasticity of substitution; Imports; Consumption; Cointegration; Generalized method of moments JEL classijicatinn: FlO; E21; C22 1. Introduction In an open economy, both the real exchange rate and the real interest rate can affect the consumption of imported goods. Shifts in the real exchange rate can *Corresponding author. Tel.: (613) 782-8827; fax: (613) 782-7163;e-mail: bamanoabank-banquecanada.ca. 0022.1996/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0022-1996(95)01418-7 440 R.A. Amano, T.S. Wirjanto I Journal of International Economics 40 (1996) 439-457 influence the current allocation of consumption between imported and domestic goods by changing their relative price. The real interest rate, on the other hand, can influence the intertemporal allocation of consumption by changing the relative price between current and future consumption. Despite the potential importance of the latter effect for determining import consumption behaviour, we are aware of only a few papers that examine the possible effect of intertemporal substitution using a formal model of optimizing behaviour.’ This paper attempts to contribute to this literature by examining the role of intertemporal substitution in import consumption using a model based on the permanent income hypothesis. Significant evidence of intertemporal substitution in import consumption would call into question conventional import models that do not account for this feature. Such evidence would suggest that, in addition to the effects of relative prices, real interest rates play an important role in determining import consumption behaviour. We consider a two-good permanent income model that is additively separable in domestically produced goods consumption (domestic consumption) and foreignproduced goods consumption (import consumption), and that allows for random preference shocks in the consumer’s utility function. There are two notable advantages from using this preference structure. First, by allowing for random preference shocks we avoid one possible factor that has been suggested as a source of empirical rejections of the consumption Euler equation (see Garber and King, 1983). Second, the additive separability structure of the utility function allows us to pursue two different estimation strategies. The first method employs the theory of cointegration to exploit the long-run restriction imposed by the first-order conditions of the model. This restriction is used to recover the preference parameters from the data.* Under reasonably general conditions, the resulting estimates can be shown to be robust to the presence of liquidity constraints, stationary but unobservable preference shocks, the form of time non-separability, heterogeneity across consumers, and non-orthogonal but stationary multiplicative measurement error. The second method consistently estimates the preference parameters from the Euler equations using the generalized method of moments (GMM) of Hansen (1982). In addition to the assumption of stationary forcing variables, GMM requires assumptions of deterministic preference shocks as well as the absence of liquidity constraints, time non-separability in preferences and measurement error. Thus, the application of these two different approaches on the same data set allows us to examine the severity of these assumptions which are often imposed in the literature. The remainder of this paper is organized as follows. Section 2 presents the general permanent income model which allows for random taste shocks and ‘See Husted and Kollintzas (1987), Gagnon (1989), Ceglowski (1991), Kollintzas and Zhou (1992) and Clarida (1994) for papers that examine import demand in a dynamic optimization framework. *Recently Ogaki and Park (1989) used the cointegration concept to estimate the preference parameters from a linear expenditure system on disaggregated commodities. R.A. Amano, T.S. Wirjanto I Journal of International Economics 40 (1996) 439-4.57 441 additive separability in domestic and import consumption. The long-run or cointegration relationship and the Euler equations implied by the model are then derived and discussed. In Section 3, we compare the cointegration and GMM estimation approaches in the presence of different economic factors. Section 4 describes the data used in this study and reports the unit-root test results. Section 5 presents empirical estimates of the intertemporal of substitution from the cointegration approach while Section 6 reports those based on the GMM approach. Section 7 concludes. 2. The model Suppose that a representative consumer faces a stochastic stream of income and chooses consumption and asset holdings to maximize expected lifetime utility (1) subject to the following period-by-period budget constraint A, = (1 + R,)A,-, + r, - P,“C, - P;M,, (2) where E, is the expectations operator based on period t information, BE (0,l) is a discount factor, C, is real consumption of domestically produced non-durable goods at time t, M, is real consumption of imported non-durable goods in period t, A,, is real financial assets at the end of period t, R, is the real interest rate on assets held between period I- 1 and I, Y, is the real non-property income (net of tax) in period t, PF is the price of import consumption and Py is the price of domestic consumption. It is assumed that U is increasing and concave in its arguments, and that U,(O,M) = U,(C,O)+m. The Lagrangian for the problem is given by m E, &“{W,,M,) - @iA, - (1 + WA,_, - Y, + P:C, + P:Md> , (3) [ t=o 1 where @l is the Lagrange multiplier associated with the budget constraint Eq. (2). The first-order conditions for period t are given by the following equations: (1 ~Py)u,,, = q, (4) (1lp:)u,,, = q3 (5) -V./T1 +RrM+~l= @L (6) for t= 1,2,. . . , where U,,=&!.J(C,,M,)laC, and lJ,,,=XJ(C,,M,)ldM,. Equating the first-order’ conditions (4) and (5) yields the static relation 442 R.A. Amano, T.S. Wirjanto J Journal of International Economics 40 (1996) 439-457 p, = uh4.t JUcp (7) where P, = PFlP,“. Substituting (4) and (5) into (6) yields the Euler equations for domestic and import consumption JqJu + R,+,)(P,HIP::1)(Uc,,+,/U,,,) - l]= 0 (8) and To exploit the empirical implications of the model, we assume that consumer preferences are additively separable, so that the period utility function is given by whereaandv~O,C~~~l(l-a)=lnC,andM~~”l(l-v)=lnM,fora=v=1,and K is a scaling factor.3 Random shocks to preferences are allowed in the above specification via the stochastic processes {A,,,}~=-m and {A,,,,}~=-m which are assumed to be stationary or I(0) processes. For this form of ut%ility, l/a may be interpreted as the long-run intertemporal elasticity of substitution (IES) for domestic consumption and l/u the corresponding IES for import consumption. Given the utility function (IO), Eq. (7), Eq. (8) and Eq. (9) can be expressed as KP,(C,-“IM;“)(A,,,//i,,,) = 1, (11) @LU+ R,)(P~IP::,)(C,+,IC,)-“(Ac,,+,lA,,> - I]= 0, (12) and (13) respectively. The Euler Eq. (1 l), Eq. (12) and Eq. (13) can be estimated separately or jointly by GMM. Consistent estimates of the preference parameters can then be obtained using stationary instruments that are in the consumer’s information set at time t, provided that the forcing variables are I(O), the preferences shocks are deterministic, and that liquidity constraints, time non-separability in preferences and measurement error are absent. For the cointegration approach, we focus on the static relation (11) which can be rewritten in logarithmic form as k + m, + (llv)p, - (alvk, = (l/d(hMM,, - A,,), (14) “The addilog utility function is commonly used in this literature. See for example Ceglowski (1991) and Clarida (1994). R.A. Amano, T.S. Wirjanto / Journal of International Economics 40 (1996) 439-457 443 where the lower-case letters denote variables in logarithmic form. If the forcing variables are I( 1) then the assumption of I(0) preference shocks implies {m, + k + (1 lv)p, - ((uIv)c,} - I(O), (15) with the cointegrating vector given by (1,l lv, - a/~)~. The cointegrating restriction in (15) motivates the following cointegrating test regression: m, = b, + b,t + b,p, + b3C, + I?,, (16) where b, = - 1lv, b, = a/v and E, is an I(0) zero mean random error termP In Eq. (16) the preference parameters, u and v, are just identified. Therefore, holding constant the marginal utility of wealth, the ratio of income elasticity of import and domestic expenditures is given by (Y/V. Notice that the identification of the IES coefficient relies on the assumption of additive separability between the two goods. If domestic consumption is not additively separable from import consumption, the IES coefficient for domestic consumption is not well defined. 3. Comparison of cointegration and GMM approaches Relative to the GMM approach, the cointegration approach for estimating IES parameters offers many advantages and requires only that the time-series data are I( 1) processes. These advantages include robustness to a number of factors such as the form of time non-separability, and the presence of stationary but unobservable preference shocks, liquidity constraints and measurement error. In this section, we compare the two different estimation approaches in the presence of these economic factors. We begin by considering the issue of time non-separable preferences. Let CT and MT be defined as the service llows from the purchases of C, and M, respectively r c; =cs,c,-, (8, = 1) i=o = 6(L)C* (17) and ‘We include a trend term in the test regression to make the distribution of the test statistic free of the unknown intercept term. In addition, we follow Clarida (1994) and argue that its inclusion allows comparison with the empirical literature estimating ad hoc import functions, and the capture of effects that are difficult to model such as quality improvements (see Feenstra, 1994). 444 R.A. Amano, T.S. Wirjanto I Journal of International Economics 40 (1996) 439-457 where C, and M, are real consumption expenditures at time t.5 Consider the utility function (10) defined over CT and A47 given by Eq. (17) and Eq. (18), where S(z) and v(z) satisfy the condition that the utility function evaluated [C,*,Af]*] be finite (as in Eichenbaumet al., 1988). Then the static first-order condition in terms of CT and Mf is (19) Suppose,for the moment, that there are no random shocks to the preferences given in (10). Then Eq. (19) implies the following conditional moment restriction, E,[e,@‘,~,a,v)] = E,[P,(l -JSL-‘)-‘CT-” - K(l -J&)-‘M,*-‘1 = 0, which involves {C~+i}~=oand {M~+i}~zo. Eq. (19) can be rewritten as E,[U,(&,w,v)] = E,[P,(l -JSL-‘)C,*-” - K(1 -JqL-‘)M,*-‘1 = 0, (20) such that the new conditional moment restriction involves C*,, C,*,i, M,* and MT+, only. However, given the assumptions about the stochastic processes generating C, and M,, Eq. (20) cannot be used as a basis for GMM estimation for the unknown preferenceparameters(a and v), unless it is suitably transformed to attain stationarity and a very restrictive form of time non-separability is imposed. The cointegration approach, on the other hand, can be used by rewriting Eq. (19) as (21) and {M~+iIMt}~z-, are all I(0) for Since&,+j>L, {A,+,t+ilY=--my {Zt+i’CtlY=-m any fixed integer i, it follows that the left-hand side of Eq. (21) is also I(0). Thus, the cointegration approachto estimating the IES parametersis not sensitive to the form of time non-separability (6). This is because the cointegration regression ‘The non-durable nature of our consumption data may call into question this approach. However, empirical studies, such as Hayaahi (1985), have found a good deal of durability in non-durable goods even at the quarterly frequency. Moreover, the NIPA definition of non-durablesincludes items such as clothing, shoesand pens, so that it may be not unreasonableto allow for somedegree of service flows. R.A. Amano, T.S. Wirjanio I Journal of International Economics 40 (1996) 439-457 445 involves variables in terms of purchases which implies that the parameters Si need not be estimated. The preference parameters can, therefore, be consistently estimated without any prior information on the form of time non-separability provided only that the time series are I( 1) processes. It is worth noting that the cointegration approach may be extended to the case of non-separable preferences. To see this, assume that the intertemporal utility function over C, and M, is given by a monotonic transformation of the utility function given in (lo), WC&f,) = +,,(r: -0 1 - 41Ac,, + w: - “41 - w,,,>, where 4’,>0 and non-separability between the two consumption goods is allowed. The static relation can be obtained as a ratio of the following two first-order conditions, that is, (l/P,)(A~,,IAc,,)(KM,“IC,“) = 1. G-9) Taking the natural logarithm of Eq. (22) and rearranging it yields the cointegration restriction or Eq. (15). While the cointegration restriction is robust to time non-separability with additive separability between the two consumption goods, and to non-separability between the two consumption goods, it is, in general, not robust to the time non-separability assumption in the absence of additive separability. Garber and King (1983) argue that unknown preference shocks can explain empirical rejections of the consumption Euler equation that often occur with the GMM approach. In contrast, the cointegration approach allows for any I(0) preference shocks. This can easily be understood by considering Eq. (14), which we reproduce below for convenience: k + m, + (l/z+, - (alv)c, = (l/~)(h~,, - A,,,). We can see from Eq. (14) that as long as the preference shocks are I(0) processes, the left-hand side of the equation will be cointegrated, allowing us to estimate consistently the preference parameters. The cointegration approach also allows for the presence of liquidity constraints. This is due to the fact that the cointegration restriction is based on the static condition in (7) which equates the marginal rate of substitution between consumption of the two goods. Unlike the Euler Eq. (8) and E@. (9), this static relation does not rely upon the assumed absence of liquidity constraints. It only relies upon the ability of the consumer to trade off consumption of the two goods at the rate P,, irrespective of the shape of the intertemporal budget constraint. In contrast, the Euler equations in (8) and (9) will be misspecified in the presence of 446 R.A. Atnano, T.S. Wirjanto I Journal of International Economics 40 (1996) 439-457 liquidity constraints because there will be an additional unobservable term in the Euler equationsP This implies that GMM estimation of the Euler equations will lead to inconsistent parameter estimates. It is well known that GMM estimates of Euler equations are generally sensitive to measurement error.’ The cointegration framework, on the other hand, allows for measurement error even when the regressors in the cointegration regression fail to be asymptotically orthogonal to the regressand. The only assumption that needs to be made is that the ratio of measurement error to its true value is an I(0) variable. To demonstrate that the cointegration restriction in Eq. (15) is not sensitive to stationary non-orthogonal measurement error, let MT be a measured variable, and EM, = (M: -M,) lM, be the ratio of the measurement error to the true variable and assume that {E,,}~=-, is I(0). Then, the natural logarithm of the measurement error given by {ln (M: -M,)}r= --m is an I( 1) process. Next, write the measured variable in terms of the true variable and the measurement error as M, + = (1 + E,,)M,, which after taking logarithms yields rn: = m, + In (1 + EM,). It follows that m,? is I( 1) since it is the sum of an I( 1) and I(0) variable. In a similar fashion, we can show that et’ and p,+ are also I( 1) variables. The previous argument allows us to express the cointegration relationship for the measured variables as [m,+ - K + (1 l~)p~+ - (a/z+;] = [m, - k + (1 IY)~, - (al~)c,] + [In (1 + EM,) - k + (1 lv) In (1 + Epz) - (a/v) In (1 + EC,)], where the first term of the right-hand side of the equality is I(0) due to the cointegration restriction imposed by the first-order condition of the model, and the second term is I(0) by assumption. This result implies that the term of the left-hand side of the equality is also I(0) and that the cointegration vector implied by the model in terms of measured quantities is given by [ 1,( 1lv), - (a/v)] r, which is the same cointegration vector implied by the model in terms of the true variable. 4. Data description and pretests for integration The data are taken from the McGraw-Hill/Data Resources Inc. U.S. database. All series are seasonally adjusted, quarterly, span the sample period 1967 Ql to 1993 Q2 and are used in logarithm form. The definitions and series names (in parentheses) are as follows. The series M, is obtained by dividing real personal consumption expenditures of non-durable imported goods, M’ (M87NIA4N), by 6The term is the Kuhn-Tucker multiplier associated with borrowing constraints scaled by marginal utility. Unfortunately, there is no tractable closed-form solution for this endogenous term. ‘The sensitivity of the GMM estimator to measurement error has been illustrated in a simple Monte Carlo study by Gregory and Wijanto (1993). R.A. Amano, T.S. Wirjanto I Journal Table I Unit-root tests: augmented Dickey-Fuller 1993 42” of International Economics 40 (1996) 439-457 (ADF) and Phillips-Perron 447 (PP) tests, sample 1967 Ql to Variable ADF lags ADF r-statistic PP Z<.-statistic Imports (m,) Relative price (p,) Consumption (c,) 0 0 1 - 2.03 - 1.54 - 1.24 - 7.84 - 3.89 -3.71 “The ADF and PP critical values are calculated from MacKinnon (1994). All test regressions include a trend term. To determine the ADF lags we use the data-dependent lag length selection procedure advocated by Ng and Perron (1995) with a 5% critical value. The initial number of AR lags is set equal to the seasonal frequency plus one or five. To estimate the long-run variance for the PP test statistic we use the VAR prewhitened quadratic kernel estimator with a plug-in automatic bandwidth parameter, as suggested by Andrews and Monahan (1992). the total population of age 16 and over (NC16#). While data on the consumption of domestically produced non-durable goods are not available, we follow Clarida ( 1994) and define C, as C, = (CN, - P;M,!)lP,H, where Clv, is non-durables consumption valued in current dollars (CN), PF is the implicit price deflator for non-durables imports (MNIA4N/M87NIA4N) and Pr is the producer price index for non-durable consumer goods (WPISOP3 120). The resulting series is then divided by the population to admit our real per capita domestic non-durables consumption measure. Finally, the relative price measure, P,, is constructed as the ratio between P,” and Py. We examine the time-series properties of the series m,, pr and c,, using the augmented Dickey and Fuller (1979) and Phillips and Perron (1988) 2, tests. These tests allow us to test formally the null hypothesis that a series is I( 1) against the alternative that it is I(0). The test statistics are reported in Table 1. For all three variables, the null hypothesis of a unit root cannot be rejected even at the 10% level of significance. Therefore we conclude that the variables under consideration are well characterized as non-stationary or I( 1) processes. This conclusion suggests that the cointegration approach for estimating the IES may be more fruitful than the GMM approach, since the former assumes I( 1) variables whereas the latter assumes stationary forcing processes. We explore this issue in the next two sections. 5. Structural parameters and cointegration The theory outlined in Section 2 together with the unit-root test results in Table 1 imply that the variables nz,, pr and c, should be cointegrated with an unique 448 R.A. Ammo, T.S. Wirjanro I Journal of International Economics 40 (1996) 439-457 cointegrating vector given by [ 1, 1/ V,- al V] ‘. Therefore, test results consistent with cointegration between the three series and an unique cointegrating vector would be evidence in favour of the model. To examine whether evidence consistent with cointegration exists, we use the two-step approach proposed by Granger (1983) and later refined by Engle and Granger (1987). Specifically, we employ the augmented Dickey-Fuller (ADF) test suggested by Engle and Granger and the Z, test proposed by Phillips and Ouliaris (1990) to test the residuals from regression (16) for stationarity or cointegration. The results of the augmented Engle and Granger (AEG) and Phillips and Ouliaris (PO) tests (Table 2) allow us to reject the null hypothesis of no cointegration in favour of the cointegration alternative at the 5% level. It is important to note that, in general, if a system of three I( 1) variables has IZ (n 53) common stochastic trends, then there are 3 -n linearly independent cointegrating vectors. It follows that if there is one single common stochastic trend among three I( 1) variables, then there are [3(3 - 1)/2] = 3 pairs of variables that are cointegrated. If, on the other hand, there are two common stochastic trends among three I( 1) variables then the cointegrating vector must be unique up to a scaling factor (see Stock and Watson, 1988). This argument suggests that we should test the null hypothesis that no combination of any two variables is cointegrated. The results for these cointegration tests are also presented in Table 2. For each pair of the three variables {( mt.c,),(m,,p,).(c,,p,)}, the AEG ad PO tests cannot reject the null of no cointegration even at the 10% level, suggesting that the cointegrating vector will be unique. The results so far allow us to conclude tentatively that the data are consistent with the predictions of the model. That is, m,, P, and c, appear to be cointegrated and the cointegrating vector of these variables appears to be unique. This allows us to proceed and estimate the IES for domestic and import consumption. Before we estimate the IES, it is important to note that the error term ct which contains the preference shock parameters is likely to be correlated with the regressors in the cointegrating regression. More specifically a temporary change in imports induced by a change in the preference shock AM,, would be likely to be correlated with the relative price of imports. Similarly, the preference shock A,, is Table 2 Residual-basedsingle-equationtests for cointegration augmentedEngle-Granger (AEG) and PhillipsOuliaris (PO) testsa Variables m,v P, and c, AEG lags AEG r-statistic PO za-statistic 0 -4.25* - 2.45 -2.05 -0.99 - 30.0s* - 8.92 -1.25 -2.98 m, and C, 0 m, and pr 0 c. and P. 1 “Henceforth, ** and * indicate significance at the 1 and 5% levels, respectively. AEG and PO Z, critical values are calculated from MacKinnon (1994). See the footnote in Table 1 for other details. R.A. Amano, T.S. Wirjanto I Journal of International Economics 40 (1996) 439-457 449 also likely to be correlated with domestic consumption. Thus, the least-squares (LS) estimator, even though it is consistent and converges to its true value at a faster rate T than the usual rate T “2, will not be efficient even asymptotically. It also has an asymptotic distribution that depends on nuisance parameters, thereby invalidating conventional inferential procedures. To control for these problems we use the estimation approaches developed by Phillips and Hansen (1990) and Stock and Watson (1993). Both these estimators possess the same limiting distribution. as full-information maximum-likelihood estimates, and hence are asymptotically optimal. Table 3 presents the parameter estimates obtained using the two efficient procedures and simple LS. Comparison of the LS estimates to the efficient estimates shows that we would have over estimated the effect of the regressors if we used only the former. We find c, and P, from both Stock and Watson (SW) and Phillips and Hansen (PH) estimators to be statistically significant and to have a priori expected signs. We also find that the SW and PH estimates are not statistically different from each other. Both approaches estimate the relative price effect to be about -0.9, and the domestic consumption effect to be roughly 1.6. These estimates are well within the range found by other researchers (see surveys in Goldstein and Kahn, 1985, and Marquez, 1990), and imply IES parameters for domestic ( 1/(u) and import ( 1lv) consumption of 0.6 and 0.9 respectively. Ogaki and Park (1989) also estimate preference parameters using the cointegration approach and find an IES estimate for U.S. non-durables of about 1.7. In their work, however, they do not distinguish between import and domestic consumption. In comparison to other studies that differentiate between the import and domestic consumption, our estimate for the IES of import consumption is quite similar whereas that for domestic consumption is somewhat larger. Ceglowski (1991) examines the role of intertemporal substitution in U.S. import demand using a two-good model based on the permanent income hypothesis. Estimation of the resulting reduced-form equations via both LS and instrumental variables approaches yields IES parameter estimates for import consumption of about 0.9 and for domestic consumption between 0.3 and 0.4. Clarida (1994) also examines U.S. import demand using a two-good version of the permanent income model. The model is used to derive a long-run equilibrium restriction that is subsequently estimated using a cointegration approach. Although the primary objective of Clarida’s investigation is not concerned with estimating IES parameters per se, we can still infer them from his results. According to these results, the implied IES Table 3 Hansen’s tests for parameter instability” Lc 0.63 MeanF SupF 7.61 15.19 “The Hansen test statistics are based on VAR(2) prewhitened Phillips and Hansen (1990) estimates. 450 R.A. Amano, T.S. Wirjanto I Journal of International Economics 40 (1996) 439-457 parameter estimates for import and domestic consumption are about 0.9 and 0.4, respectively. Thus, our cointegration results tend to confirm those in Clarida (1994) with a slightly different and longer data set. It should be noted, however, that these IES estimates (including our own) imply that the income elasticity for domestic consumption is significantly lower than that for import consumption; a result that is difficult to reconcile with economic theory. This suggests that the observed intertemporal response of import consumption may also embody the response of other economic agents, possibly those attributable to the intertemporal behaviour of importers’ inventories.’ Nevertheless, the fact that our estimates produce a significant and positive IES for import consumption suggests that intertemporal substitution is an important feature of import consumption behaviour. Finally, for the purpose of interpreting the elasticities it is important that the long-run parameter estimates be structurally stable over the sample period. To this end we apply three tests of parameter constancy for I( 1) processes recently proposed by Hansen (1992) - the Lc, MeanF and SupF tests. All three tests have the same null hypothesis of parameter stability, but differ in their alternative hypothesis. Specifically, the SupF is useful if we are interested in testing whether there is a sharp shift in the regime while the Lc and MeanF tests are useful for determining whether or not the specified model captures a stable relationship. According to Hansen (1992) these tests may also be viewed as tests for the null of cointegration against the alternative of no cointegration. The results from Hansen’s tests (Table 4) suggest that the cointegrating vector is stable over the sample period and that we are unable to reject the null of cointegration at the 5% level. The latter provides support for our previous conclusion that the variables under Table 4 Cointegration estimates of the structural parameters” Variable LSb PH’ SWd Constant -6.091 P, - 1.032 c, 1.712 Trend 0.020 -5.932** (0.304) -0.895** (0.114) 1.640** (0.167) 0.019** (0.001) - 5.614** (0.216) -0.893** (0.073) 1.505** (0.117) 0.019** (0.001) “Standard errors are in parentheses. bLS =least-squares estimator. ‘PH (Phillips and Hansen, 1990) estimates are based on the VAR(2) prewhitened quadratic kernel estimator with a plug-in automatic bandwidth parameter procedure proposed by Andrews and Monahan (1992). ‘SW (Stock and Watson, 1993) estimates are based on fourth-order leads and lags and the Bartlett kernel as proposed by Newey and West (1987). %Jnfortunately, dam limitations prevent us from exploring this issue. R.A. Amano, T.S. Wirjanto I Journal of International Economics 40 (1996) 439-457 451 consideration are cointegrated while the former implies that our estimates of the IES are stable. 6. Structural parameters and GMM In this section we estimate the IES from the Euler Eq. (1 l), Eq. (12) and Eq. (13) using GMM. As previously mentioned, for GMM to estimate consistently the structural parameters from these Euler equations, we must assume, in addition to stationary forcing variables and deterministic preference shocks (that is, A,,,=A, and AM,, =A,Vt), the lack of liquidity constraints, time non-separability, and measurement error. These assumptions are likely to be violated in practice but are often made in the literature (for instance, the univariate results reported in Table 1 suggest that the data under consideration are non-stationary or I( 1) processes). Given these assumptions, we can rewrite the Euler Eq. (1 l), Eq. (12) and Eq. (13) as K*(C,“IM,“)(P;IP;) = 1, &V(l -tR,)(P~IP::,)(C,+,IC,)~” (23) - 11=o, (24) and -W(l +R,)(P~IP~+,)(M,+,IM,)~“- II=0 (25) respectively, where K” = K(A,lA,). These equations can be estimated separately or jointly using an instrument set that includes a constant, C, /C,- , , R,- , , M, lM,- , , PF,-,,lP: and P:mI /Py, and their lags. The real interest rate is calculated as R, = [( 1 - 0.3)i,] lP, where 0.3 is the assumed marginal tax rate and i, is the 90-day U.S. Treasury bill rateP Overall the results are not very encouraging. Table 5 presents the results for single-equation GMM estimation of the three equations. The upper part of the table corresponds to parameter estimates using an instrument set lagged one period whereas the lower panel are those for instruments lagged two periods. In both cases, the J-tests for over-identifying restrictions are rejected at the 1% level. Moreover, the estimates of the IES appear implausible. For instance, singleequation estimation of (23) would give us IES for domestic and import consumption of about 1.3 and 4.3, respectively. Table 6 provides the joint GMM estimation results. Again the J-tests reject the model at low percentage levels, and the IES estimates are either too large or of the wrong sign (though not ‘The following GMM results are broadly representative of different values of the marginal tax rate and many combinations of the instruments and their lags. Table 5 GMM estimates of the structural parameters: single-equation estimation” Equation I%(standard error) (23) 0.774** (0.227) -5.443 (3.130) .Y C (standard error) J-test (degree of freedom) Instruments lagged one period (24) (25) 0.231* (0.111) 0.937 (1.013) Instruments lagged two periods (23) (24) (25) 0.709** (0.213) - 3.089 (4.145) 0.233 * (0.091) - 1.230 (1.761) “GMM estimation is performed with the Bartlett kernel and the truncation parameter set equal to one. 21.153** (4) 21.788** (4) 19.837** (4) 20.765** (4) 19.503** (4) 18.864** (4) 2 5: 9 F L E” 3 fl 9 3 R 2 0z. is. P s $. h G 3 2 $ 9 R.A. Amano, T.S. Wirjanto I Journal of International Economics 40 (1996) 439-457 453 454 R.A. Amano, T.S. Wirjanto I Journal of International Economics 40 (1996) 439-457 significantly). For example, if we look at the joint estimation of all three equations we find IES of about 1.4 and 4.3 for domestic and import consumption. To summarize the GMM results, we find very little evidence to support the model when the Euler equations are estimated by GMM, and we also find estimates of the IES that appear implausible. At a technical level, the poor performance of the GMM estimator documented above may be due to the non-stationary nature of the forcing variables. In this case, the GMM estimates of the non-stationary components would be likely to generate non-trivial secondorder bias (see Phillips, 1991 for discussion). Economically, these results suggest that assumptions often made in the literature about deterministic preference shocks, and the absence of liquidity constraints, time non-separability and measurement error, may be too restrictive. It is difficult, however, to discern which economic factor or factors are responsible for the weak GMM results. Nevertheless, a review of some recent studies examining different aspects of U.S. consumption behaviour may help shed some light on the possible sources that have led to our rejection of the Euler equations. One strand of the consumption literature examines the importance of time non-separable preferences for determining the behaviour of U.S. consumption. Dunn and Singleton (1986) and Eichenbaum et al. (1988) study monthly U.S. aggregate consumption data and find evidence in favour of time non-separability in the form of local durability. In contrast, Ferson and Constantinides (1991) find that time non-separability in the form of habit persistence is an important feature of annual, quarterly and monthly U.S consumption data. Braun et al. (1993) confirm this finding. In short, while there appears to be some consensus pertaining to the importance of time non-separable preferences, there is much less consensus concerning the way that time non-separable preferences manifest themselves in U.S. aggregate consumption. Another strand of the literature explores whether rejections of the permanent income model are due to the presence of binding liquidity constraints for some consumers. Flavin (1985) examines whether excess sensitivity of consumption is due to liquidity constraints or myopia, and finds evidence in favour of the liquidity constraints hypothesis. Bean (1986) and Cushing (1992) find similar empirical support for the hypothesis that a significant proportion of U.S. consumers faces binding borrowing restrictions. Antzoulatos (1994) shows that the finding of Campbell and Mankiw (1990) that about 50% of U.S. consumers are ‘rule of thumb’ consumers is actually due to the presence of liquidity constraints. Similarly, a number of authors, such as Mankiw et al. (1985), attribute their rejection of the permanent income model to the possible presence of liquidity constraints. It seems, therefore, that liquidity constraints are an important feature of U.S. consumption behaviour, and that the estimates obtained from the Euler equations via GMM are likely to be inconsistent. Finally, Mankiw et al. (1985), among others, argue that studies which examine aggregate consumption behaviour are subject to measurement error since the R.A. Amano, T.S. Wirjanto / Journal of International Economics 40 (1996) 439-457 455 variables under consideration are typically proxies for the true variables. In fact, it would not be difficult to argue that most empirical work suffers from some degree of measurement error. In the current paper, the variable M, is defined in terms of non-durable consumer imports, which is not the same as consumption of nondurable imports. Since M, is also used to construct C,, it is likely that both our proxies for consumption are measured with error, and that not accounting for these measurement errors in estimation could result in misleading conclusions. To the extent that we can draw inferences from U.S. aggregate consumption studies, it appears that our rejection of the Euler equations may be due to the presence of time non-separable preferences, liquidity constraints and measurement errors. The U.S. aggregate consumption literature does not allow us, at this moment, to rule out any of these factors as possible explanations for our weak GMM results. 7. Conclusions This paper attempts to estimate the degree of intertemporal substitution in import consumption using a permanent income model that allows for random preference shocks and for additive separability between domestic and import consumption. The latter feature allows us to apply two different estimation approaches. The first approach is based on the theory of cointegration. Under reasonably general conditions, the resulting estimates can be shown to be robust to the presence of liquidity constraints, stationary but unobservable preference shocks, the form of time non-separability, heterogeneity across consumers, and non-orthogonal but stationary multiplicative measurement error. The second approach based on GMM requires us to assume stationary forcing variables and deterministic preference shocks, in addition to the absence of liquidity constraints, time non-separability in preferences and measurement error. Thus, the two different estimation approaches allow us to assess the severity of these assumptions often made in the literature. The estimation results lead us to three tentative conclusions. First, the evidence from the cointegration approach suggests that intertemporal substitution is an important feature of import consumption and that conventional import models that do not account for this feature may be called into question. Using the cointegration approach, we found plausible estimates of the IES for domestic and import consumption of about 0.6 and 0.9, respectively - well within the range of previous estimates. Second, the GMM results suggest that the assumptions often made in the literature, when researchers attempt to recover IES from Euler equations estimated by GMM, may be one explanation why reasonable estimates of the structural parameters are often difficult to obtain. Using the GMM approach with the accompanying assumptions gave us J-tests that tend to reject the model and IES estimates that appear implausible. Third, the plausibility of the cointegration 456 R.A. Anumo, T.S. Wirjanto I Journal of International Economics 40 (1996) 439-457 estimates relative to the GMM estimates suggests that our cointegration approach, which does not require the same assumptions as GMM estimation, may be a useful alternative to pursue for estimating IES using aggregate time series in other economic environments. Acknowledgments Most of this research was undertaken while the first author was with the International Department of the Bank of Canada. We thank two referees for useful comments and Bruce Hansen for his I( 1) processes structural instability tests code written in GaussTM. This paper represents the views of the authors and should not be interpreted as reflecting those of the Bank of Canada or its staff. Any errors and/or omissions are ours. References Andrews, D.W.K. and J.C. Monahan, 1992, An improved heteroskedasticity and autocorrelation consistent covariance matrix estimation, Econometrica 60, 953-966. 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